To understand information processing in the brain, it is important to identify the aspects of neuronal responses that carry information important for stimulus coding, and how that information is used for stimulus identification and recognition in cognitive processes. The number of spikes emitted by a neuron varies with experimental condition, and all that we know about how neurons work indicates that these spike trains are responsible for carrying information quickly over distances from several millimeters to many decimeters (e.g., into the spinal cord). To describe a neuronal response completely we would need to keep track of the arrival time of each spike. We have shown that all of the information carried by neuronal spike trains requires specifying only the spike count distribution (which is approximately truncated Gaussian), the variation in firing rate with a bandwidth of less than 30 Hz (equivalent of measuring spike counts in 30 ms wide bins), and the peristimulus-time histogram, that is, how the firing rate changes over time. The spike count distribution (that is, knowing how many times each spike count occurs) is important because our assessment of temporal coding depends on the spike count. Intuitively this seems clear when we realize that the more spikes that are present, the richer the potential temporal code. Thus, the influence of variation in the number of spikes that occurs with successive presentations of a stimulus must be taken into account properly when estimates of neuronal coding are made. If the responses arise from a random process with a certain overall pattern in time, the responses must follow well-known statistical rules that are described by order statistics. The order statistic representation allows exact knowledge of the amount of information carried by neuronal responses if the spike count distribution and the average variation of firing rate can be measured. Using a straightforward reformulation of the basic formula of order statistics, we derived a decoder that decodes neuronal responses millisecond-by-millisecond as the response evolves. This algorithm can form the basis of an instant-by-instant neuronal controller. Decoding spike trains can be thought of as looking them up in a dictionary. Order statistics can be calculated for any distribution of spike counts, and experimental data can support a wide variety of models of the spike count distributions. Modeling the observed spike counts as a mixture of several (typically 1-3) Poisson lets us think of the spike trains as having arisen from a mixture of Poisson processes. The theory of Poisson processes can then be used to calculate order statistics much more efficiently than possible for an arbitrary distribution of spike counts, which substantially increases decoding speed. Given these accurate statistical models of neural responses, we studied what happens when they are applied to small populations (pairs) of neurons. Our measurements in primary motor cortex, primary visual cortex, and inferior temporal cortex show that all of the patterns of spikes including simultaneous spikes are related to the same measurements, i.e. the rate variation and the spike count distribution, plus the correlations of the spike counts taken over 100's of milliseconds. Thus, the patterns of spikes are directly related to variations in firing rate, and there do not appear to be any mechanisms entraining the spikes to fire at particular, exactly specified times. In the past we used previously developed mathematical techniques to explore how the statistical methods we have used can give insight into development of biophysical models of neuronal information processing. One approach has been to learn what levels of interactions among spikes are important, and how closely our Poisson based model describes data. To do this we have compared our model to another similar model by Kass and Ventura using Nakahara-Amari information geometry. This approach allows the evaluation of the differences between statistical models in a single framework. We have also been using a mean-field approach to approximate the activity of a small (~10000) population of neurons to determine whether simple descriptions of stochastic biophysically realistic networks match the properties of the data we typically collect. These two mathematical approaches have helped to confirm that our order-statistics based model matches our experimental data quite closely. This latter approach is allowing us to explore the source of unexpected trial-to-trial variability that occurs in neuronal responses in dopamine-rich brain regions during reward seeking behavior. In work seeking to learn how visual images are remembered we have studied neuronal responses in the inferior temporal cortex area TE during a delayed stimulus matching task. We measured the correlations between trial-by-trial fluctuations in different task phases (sample, nonmatch, and match). The sample and match response fluctuations correlated more strongly than sample and nonmatch fluctuations, even though the interval between sample and nonmatch was shorter than the interval between sample and match (median variance explained: sample vs. match = 7.3%; sample vs. nonmatch = 1.9%). Such trial-by-trial correlation between sample and match responses is strong evidence for local storage of the short-term memory trace. There seems to be no way to explain these correlations if the TE neurons only encode the stimulus, because noise in encoding appears to be independent across different stimulus presentations, and thus can not preserve fluctuations across events. Here we propose that these correlations are a signature for iconic, short-term memory: these TE neurons hold the memory trace of the sample image in the strength of its synaptic inputs using a form of one-trial-learning. In this model synaptic weights are slightly modified when a stimulus to be remembered is presented. A population of neurons operating using this mechanism forms a matched filter (the best filter for detecting the presence of a known signal in white noise) for the sample image. When incoming responses elicited by subsequent presented stimuli interact with these altered synapses, the output reflects an effect to the noise that was stored with the signal. The power in the responses of the population of TE neurons, but not in individual neurons, is higher for the match than for the nonmatch stimulus. This new theory is consistent with an idea we proposed in 1992 (Eskandar et al.), when we showed that responses of IT cortex neurons contained information about the sample and current images in a DMS task.